The six educated frogs in the illustration are
trained to reverse their order, so that their numbers shall read 6, 5,
4, 3, 2, 1, with the blank square in its present position.
They can
jump to the next square (if vacant) or leap over one frog to the next
square beyond (if vacant), just as we move in the game of draughts, and
can go backwards or forwards at pleasure.

Can you show how they perform
their feat in the fewest possible moves?

It is quite easy, so when you
have done it add a seventh frog to the right and try again.
Then add
more frogs until you are able to give the shortest solution for any
number.
For it can always be done, with that single vacant square, no
matter how many frogs there are.